function res = stable_leapfrog_onestep(u1,u2,N,mu,x_max,a)
h = x_max/N;
u1 = fill_ghostcell_period(u1,N,1);
res = (1+mu*h*a)/(1-mu*h*a)*u2(1:N+1) + mu/(1-mu*a*h)*(u1(3:N+3) -u1(1:N+1));